Determination of the binding energies of the np Rydberg states of H2, HD, and D2 from high-resolution spectroscopic data by multichannel quantum-defect theory

Photolysis Production and Spectroscopic Investigation of the Highest Vibrational States in H2 (X1Σg+ v = 13, 14)

Rovibrational quantum states in the X1Σg+ electronic ground state of H2 are prepared in the v = 13 vibrational level up to its highest bound rotational level J = 7, and in the highest bound vibrational level v = 14 (for J = 1) by two-photon photolysis of H2S. These states are laser-excited in a subsequent two-photon scheme into F1Σg+ outer well states, where the assignment of the highest (v,J) states is derived from a comparison of experimentally known levels in F1Σg+, combined with ab initio calculations of X1Σg+ levels. The assignments are further verified by excitation of F1Σg+ population into autoionizing continuum resonances, which are compared with multichannel quantum defect calculations. Precision spectroscopic measurements of the F-X intervals form a test for the ab initio calculations of ground state levels at high vibrational quantum numbers and large internuclear separations, for which agreement is found.

Determination of the Interval between the Ground States of Para- and Ortho-H_{2}

Nuclear-spin-symmetry conservation makes the observation of transitions between quantum states of ortho- and para-H_{2} extremely challenging. Consequently, the energy-level structure of H_{2} derived from experiment consists of two disjoint sets of level energies, one for para-H_{2} and the other for ortho-H_{2}. We use a new measurement of the ionization energy of para-H_{2} [E_{I}(H_{2})/(hc)=124 417.491 098(31)  cm^{-1}] to determine the energy separation [118.486 770(50)  cm^{-1}] between the ground states of para- and ortho-H_{2} and thus link the energy-level structure of the two nuclear-spin isomers of this fundamental molecule. Comparison with recent theoretical results [M. Puchalski et al., Phys. Rev. Lett. 122, 103003 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.103003] enables the derivation of an upper bound of 1.5 MHz for a hypothetical global shift of the energy-level structure of ortho-H_{2} with respect to that of para-H_{2}.

Nonrelativistic energy levels of D2

Nonrelativistic energies of the deuterium molecule, accurate to 10-7-10-8 cm-1 for all levels located up to 8000 cm-1 above the ground state, are presented. The employed nonadiabatic James-Coolidge wave functions with angular factors enable the high accuracy to be reached regardless of vibrational or rotational quantum number. The derivative of the energy with respect to the deuteron-to-electron mass ratio is supplied for each level, which makes the results independent of the future changes in this physical parameter and will enable its determination from sufficiently accurate experimental data.

Benchmarking Theory with an Improved Measurement of the Ionization and Dissociation Energies of H_{2}

The dissociation energy of H_{2} represents a benchmark quantity to test the accuracy of first-principles calculations. We present a new measurement of the energy interval between the EF ^{1}Σ_{g}^{+}(v=0,N=1) state and the 54p1_{1} Rydberg state of H_{2}. When combined with previously determined intervals, this new measurement leads to an improved value of the dissociation energy D_{0}^{N=1} of ortho-H_{2} that has, for the first time, reached a level of uncertainty that is 3 times smaller than the contribution of about 1 MHz resulting from the finite size of the proton. The new result of 35 999.582 834(11)  cm^{-1} is in remarkable agreement with the theoretical result of 35 999.582 820(26)  cm^{-1} obtained in calculations including high-order relativistic and quantum-electrodynamics corrections, as reported in the following Letter [M. Puchalski, J. Komasa, P. Czachorowski, and K. Pachucki, Phys. Rev. Lett. 122, 103003 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.103003]. This agreement resolves a recent discrepancy between experiment and theory that had hindered a possible use of the dissociation energy of H_{2} in the context of the current controversy on the charge radius of the proton.

Hyperfine-interaction-induced g/u mixing and its implication on the existence of the first excited vibrational level of the A + Σ u + 2 state of H 2 + and on the scattering length of the H + H+ collision

Ab initio calculations of the energy level structure of H 2 + that include relativistic and radiative corrections to nonrelativistic energies and the diagonal part of the hyperfine interaction have predicted the existence of four bound rovibrational levels [(v = 0, N = 0 - 2) and (v = 1, N = 0)] of the first electronically excited ( A +   Σ u + 2 ) state of H 2 + , the (v = 1, N = 0) level having a calculated binding energy of only E _b = 1.082 219 8(4)·10^-9 E_h and leading to an extremely large scattering length of 750(5) a₀ for the H⁺ + H collision [J. Carbonell et al., J. Phys. B: At., Mol. Opt. Phys. 37, 2997 (2004)]. We present an investigation of the nonadiabatic coupling between the first two electronic states ( X +   Σ g + 2 and A +   Σ u + 2 ) of H 2 + induced by the Fermi-contact term of the hyperfine-coupling Hamiltonian. This interaction term, which mixes states of total spin quantum number G = 1/2, is rigorously implemented in a close-coupling approach to solve the spin-rovibronic Schrödinger equation. We show that it mixes states of gerade and ungerade electronic symmetry, that it shifts the positions of all weakly bound rovibrational states of H 2 + , and that it affects both the positions and widths of its shape resonances. The calculations demonstrate that the G = 1/2 hyperfine component of the A⁺ (v = 1, N = 0) state does not exist and that, for G = 1/2, the s-wave scattering lengths of the H⁺ + H(1s) collision are -578(6) a₀ and -43(4) a₀ for the F = 0 and F = 1 hyperfine components of the H(1s) atom, respectively. The binding energy of the G = 3/2 hyperfine component of the A⁺ (v = 1, N = 0) state is not significantly affected by the hyperfine interaction and the corresponding scattering length for the H⁺ + H(1s, F = 1) collision is 757(7) a₀.

Dissociation Energy of the Hydrogen Molecule at 10^{-9} Accuracy

The ionization energy of ortho-H_{2} has been determined to be E_{I}^{o}(H_{2})/(hc)=124 357.238 062(25)  cm^{-1} from measurements of the GK(1,1)-X(0,1) interval by Doppler-free, two-photon spectroscopy using a narrow band 179-nm laser source and the ionization energy of the GK(1,1) state by continuous-wave, near-infrared laser spectroscopy. E_{I}^{o}(H_{2}) was used to derive the dissociation energy of H_{2}, D_{0}^{N=1}(H_{2}), at 35 999.582 894(25)  cm^{-1} with a precision that is more than one order of magnitude better than all previous results. The new result challenges calculations of this quantity and represents a benchmark value for future relativistic and QED calculations of molecular energies.

Electron-Nuclear Coupling through Autoionizing States after Strong-Field Excitation of H_{2} Molecules

Channel-selective electron emission from strong-field photoionization of H_{2} molecules is experimentally investigated by using ultrashort laser pulses and a reaction microscope. The electron momenta and energy spectra in coincidence with bound and dissociative ionization channels are compared. Surprisingly, we observed an enhancement of the photoelectron yield in the low-energy region for the bound ionization channel. By further investigation of asymmetrical electron emission using two-color laser pulses, this enhancement is understood as the population of the autoionizing states of H_{2} molecules in which vibrational energy is transferred to electronic energy. This general mechanism provides access to the vibrational-state distribution of molecular ions produced in a strong-field interaction.

Observation of g/u-symmetry mixing in the high-n Rydberg states of HD

The structure and dynamics of high-n Rydberg states belonging to series converging to the (v(+) = 0, N(+) = 0-2) levels of the X(+) (2)Σ(g)(+)electronic ground state of HD(+) were studied by high-resolution spectroscopy from the GK (1)Σ(g)(+) (v = 1, N = 1) state under field-free conditions. Three effects of g/u-symmetry breaking were detected: (i) Single-photon transitions from the GK (v = 1, N = 1) state of gerade symmetry to the 30d21 and 31g22 Rydberg states of gerade symmetry were observed after careful compensation of the stray electric fields. (ii) The singlet 61p12 Rydberg state of ungerade symmetry was found to autoionize to the N(+) = 0, ℓ = 2 ionization continuum of gerade symmetry with a lifetime of 77(10) ns. (iii) Shifts of up to 20 MHz induced by g/u-symmetry mixing were measured for members of the np11 Rydberg series which lie close to nd21 Rydberg states. These observations were analyzed in the framework of multichannel quantum-defect theory. From the observed level shifts, the off-diagonal eigenquantum-defect element μ(pd) of singlet-π symmetry was determined to be 0.0023(3) and the corresponding autoionization dynamics could be characterized. The ionization energy of the GK (v = 1, N = 1) state of HD was determined to be 12 710.544 23(10) cm(-1).